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I am looking for a game mechanic for a game I am designing, that would let players randomly select other players, but that by the end of the game all the players were selected equally.

My first instinct was the destiny deck from Cosmic Encounters. In that game there is a deck with a few cards representing each player. On their turn the player draws a card, and interacts with the selected opponent.
The limitation of this solution is that sometimes players select themselves. Cosmic encounters solves this by having rules for how to interact with yourself, but my game lacks this. Even if i was to simply put the card on the bottom of the deck and draw a new one, there is a chance with the last card being left of the last player who must take the last turn. At this point selecting another player randomly would unbalance the game, giving them an extra time they are selected.
Is there any other mechanic that can be used to solve this?
(I am in no way set on using cards. Any mechanic would be OK)

Could you remove cards instead of just putting them on the bottom? This might help remove the potential for a player being selected "more times than is fair" - if there are only 3 red cards in the deck, and one is removed every time they are selected, there is no possibility of red being selected a fourth time...
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thesunneversetsApr 20 '12 at 15:15

Do you want "all the players should be selected equally" by player or for the game as a whole?" (or suggestions for both possibilities?) My answer below was by player but perhaps that's not what you meant?
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Joe GoltonApr 20 '12 at 15:21

Another clarification: is the selected player open information for all players or is he/she only known by the selecting player? @thesunneversets i like this idea because it's the closest to the described scenario, but this only works if the selected player is open information, hence my question.
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rahzarkApr 20 '12 at 16:02

@thesunneversets I only put cards on the bottom if a player draws himself. He then draws another card
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AndreyApr 20 '12 at 16:15

@Andrey I think he was suggesting you remove every card EXCEPT when players select themselves. In that case just put the card in the bottom. In any case, this can lead to players knowing when each card is coming around.
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rahzarkApr 20 '12 at 16:23

6 Answers
6

If it is acceptable that the order of the players turns is different every round, you could have a deck with a card for each player, then draw the top card and let that player have the next card as target, and then the next player takes the third card as target.
Finally the last player uses the first one as target. This way each player is the target exactly once in every round.

Sounds like a good use for a bag of items - pawns colored per player, tokens, whatever you prefer. When you need to randomly select an opponent, draw one. If it's yourself, set it aside so you won't draw it again, then add it back in after you finish drawing.

...but of course, the situation you're trying to create isn't exactly ideal. If you reach the last player, and the only option left is that player, you're stuck. If you're okay with creating a little bit of inequality in player selection in this somewhat rare case, you could with it in an approximate way - if you do get stuck, just refill the bag and draw again. Otherwise, if you can handle a tiny bit of extra information (which is theoretically public to players with good memories), you could just draw the last two on the second-to-last turn, and swap the order if necessary. This isn't foolproof; the last two could both be for one of the last two players... but it might be good enough - and you could fall back to refilling the bag.

Edit: One other way to deal with potentially getting stuck: if you're okay with this kind of information, just leave the pieces out after being drawn in stacks/rows, so that you know how many are left of each in the bag. This is again something that an observant player could already know. You can then figure out if you need to do something besides draw randomly at the end.

If you don't like any of this, I'm afraid there's not much you can do besides carefully constructing a deck at the beginning of the game.

If you're happy with the way everything is working except for this edge case, you could just make it so the last 2 cards are drawn simultaneously. The second to last player gets the first card drawn unless the last player would end up with him/herself, in which case they switch.

Love this answer! Using relative positions is elegant and works for every different variation discussed in the comments! Simply wonderful :D
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rahzarkApr 21 '12 at 1:53

i don't think this is in any way different than Joe Golton's
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AndreyApr 21 '12 at 3:46

2

Yeah, I don't think this idea was thought through. If every player has their own deck constructed separately, which selects the other players equally, relative positions are entirely equivalent to absolute positions. And if you're thinking of shuffling then dealing the relative positions, there's no longer any guarantee of equal selection.
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JefromiApr 21 '12 at 17:00

@Jefromi You are right, and I didn't think my comment that throughly as well. :( If every player has it's deck it's the same as non-relative positions. And if the deck is shared, than there is no telling the distribution will be the same. I shouldn't be so quick to vote answers up!
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rahzarkApr 21 '12 at 19:19

One possibility is a separate destiny deck for each player. If you make the game for 6 players, then each player would have a "destiny deck" that includes the other 5 players. In games with fewer than 6 players, then the player colors not used are removed from all the destiny decks (though even if they forget, they can be discarded when drawn during the game).

To facilitate faster game starts, it would be nice to color code each destiny deck. So the red player would have a red on the back, color of another player on the front.

Your suggestion creates a different scenario than the one described. With a deck for each player it basically means that every player will end up selecting each other at least once. With a single deck that may never happen, because I may never stumble on a certain player's card because other players keep selecting it and I keep "skipping" it. I'm not saying it is better or worse, only different :)
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rahzarkApr 20 '12 at 15:03

@rahzark I don't think the question was specific on whether "all the players should be selected equally" by player or for the game as a whole. If the intention is to do it as a whole, then I think the mechanics end up being more complicated, which is why I opted for this one.
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Joe GoltonApr 20 '12 at 15:19

@rahzark This would work, but i feel like it would make the game a lot more boring. I am hoping for a solution that would let interactions be more random
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AndreyApr 20 '12 at 16:18

Have one deck, with X cards for each player. When you need to select a random player draw a card from the deck. If you draw yourself, draw again. Shuffle any cards drawn for yourself back in and discard the card you drew for another player. Since each player draws from the same deck, in general everyone will get picked the same amount. The exception would be if one player is drawing from the deck more than other players the deck may eventually be JUST their cards. So you'll need to make sure that X is large enough to avoid a reshuffle unless a) everyone chooses other players evenly, or a small amount of unevenness is acceptable.